Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1056 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26031382 | C2 | semidirect |
| 3. #26030712 | C2 | semidirect |
| 4. #26019398 | C2 | semidirect |
| 5. #26019369 | C2 | semidirect |
| 6. #26018668 | C2 | semidirect |
| 7. C89×#1543 | C2 | semidirect |
| 17. C2×#15668012 | C22 | semidirect |
| 20. #19151977 | C22 | semidirect |
| 24. #19151889 | C22 | semidirect |
| 25. C4×#13083558 | C22 | semidirect |
| 26. #19151325 | C22 | semidirect |
| 28. #431×C89 | C22 | semidirect |
| 29. #333×C89 | C22 | semidirect |
| 177. #1543 | D89 | semidirect |
| 179. C89 | #18715 | semidirect |
| 198. #431 | C2×D89 | semidirect |
| 200. #333 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034657 | 2 |
| #26031382 | 2 |
| #26030712 | 2 |
| #26019398 | 2 |
| #26019369 | 2 |
| #26018668 | 2 |
| C89×#1543 | 2 |
| #18715 | 89 |